Write expressions for the length and width of a rectangle that has an area equal to 3x^2-5x+2.

Answer:

3/8

Step-by-step explanation:

3/4 x 2/4 = 3/8 as a fraction form.

Answer:

3/8

Step-by-step explanation:

Answer:

Your answer is correct, it is 8x+37.

Step-by-step explanation:

The factored expression of 8 + 12 is 4 * (2 + 3) and the factored expression of 120 + 300 is 60 * (2 + 5)

Rewrite 8 + 12 using the GCF and factoring.

The expression is given as:

8 + 12

Express 8 and 12 as the products of the factors.

So, we have:

8 + 12 = 4 * 2 + 4 * 3

Factor out 4 in the above expression

8 + 12 = 4 * (2 + 3)

Hence, the factored expression of 8 + 12 is 4 * (2 + 3)

Rewrite 120 + 300 using the GCF and factoring.

The expression is given as:

120 + 300

Express 120 and 300 as the products of the factors.

So, we have:

120 + 300 = 60 * 2 + 60 * 5

Factor out 60 in the above expression

120 + 300 = 60 * (2 + 5)

Hence, the factored expression of 120 + 300 is 60 * (2 + 5)

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True. depending on the circumstances, the dequeue method of our linkedqueue class sometimes throws the queueunderflowexception

The dequeue method of a LinkedQueue class throws a QueueUnderflowException when the queue is empty, and the user attempts to remove an element from it. This is because removing elements from an empty queue is not allowed and violates the basic properties of a queue data structure. Therefore, depending on the circumstances, the dequeue method may throw a QueueUnderflowException to indicate that the operation is invalid.

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Answer: 4

Step-by-step explanation: Divide 28 by 7

Answer: 765

Step-by-step explanation:

Based on the computed 95% confidence interval, we can conclude that we are 95% confident that the true population mean falls within the range of 12.65 to 25.65.

A confidence interval is a range of values that provides an estimate of the true population parameter. In this case, we are interested in estimating the population mean (μ). The 95% confidence interval, as mentioned, is given as 12.65 ≤ μ ≤ 25.65.

Interpreting this confidence interval, we can say that if we were to repeat the sampling process many times and construct 95% confidence intervals from each sample, approximately 95% of those intervals would contain the true population mean.

The confidence level chosen, 95%, represents the probability that the interval captures the true population mean. It is a measure of the confidence or certainty we have in the estimation. However, it does not guarantee that a specific interval from a particular sample contains the true population mean.

Therefore, based on the computed 95% confidence interval, we can conclude that we are 95% confident that the true population mean falls within the range of 12.65 to 25.65.

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490

472 <490<500

it fits the criteria

Answer:

59

Step-by-step explanation:

Its easy

It takes 0.152 liters of gasoline to drive 111 kilometers at the same rate Amelia drove.

To find the number of kilometers Amelia drove per liter of gasoline, we can divide the total distance traveled (484848 kilometers) by the total amount of gasoline used (666 liters).

Kilometers per liter = Total distance / Total gasoline used

Kilometers per liter = 484848 km / 666 L

Kilometers per liter ≈ 728.73 km/L

So, Amelia drove approximately 728.73 kilometers per liter of gasoline.

To determine how many liters it takes to drive 111 kilometers at the same rate, we can use the inverse of the kilometers per liter value.

Liters for 111 kilometers = 111 km / (Kilometers per liter)

Liters for 111 kilometers = 111 km / 728.73 km/L

Liters for 111 kilometers ≈ 0.152 L

Therefore, it would take approximately 0.152 liters of gasoline to drive 111 kilometers at the same rate.

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Answer:

can you tell me please

Step-by-step explanation:

nicest

The domain for the given graph is obtained as {1, 2, 3, 4}.

A function y = f(x) is a one to one relationship between two sets X and Y where the set X is called the domain and Y the range of function f(x) ans x ∈ X and y ∈ Y.

From the graph of the given exponential function,

The set of ordered pairs can be written as follows,

{(1, 10), (2, 20), (3, 40), (4, 80)}

Since the domain is the set of first elements for a given pair of ordered set.

The domain is given as {1, 2, 3, 4}.

Hence, the domain obtained from the given graph is {1, 2, 3, 4}.

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The graph missing in the question is attached here.

Answer:

60 muffins

Step-by-step explanation:

Find out how much ml you need for each ingredient.

20 muffins =

220 ÷ 20 = 11 (milk)

250 ÷ 20 = 12.5 (castel sugar)

400 ÷ 20 = 20 (flour)

Find out the greatest number of muffins Jack can make.

1 litre = 1000 ml

1000 ÷ 11 = 90.90 (recurring decimal) (milk)

750 ÷ 12.5 = 60 (castel sugar)

1500 ÷ 20 = 75 (flour)

Find the smallest answer out of the 3 questions.

The calculated value of  the temperature now is -2°C

From the question, we have the following parameters that can be used in our computation:

Using the above as a guide, we have the following:

The temperature now is the difference of the initial temperature and the change in temperature

So, we have

Now = 15°C - 17°C

Evaluate the difference

Now =  -2°C

Hence, the value of  the temperature now is -2°C

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The given argument proves that if √√ is not transcendental over Q, then it must be algebraic over Q. By manipulating the equation and showing that √√ satisfies a polynomial equation with rational coefficients, the proof establishes the algebraic nature of √√ over Q, contradicting its assumed transcendental property.

The proof begins by assuming that √√ is not transcendental over Q. It then proceeds to show that √√ must be algebraic over Q. This is done by constructing a polynomial equation f(x) = Q[x] such that f(√√) = 0.

In the third step, the proof notes that all odd-degree terms involve √√ and all even-degree terms involve √. By moving all odd-degree terms to the right side, we obtain an equation where only even-degree terms involve √.

Next, the proof factors √ out from the terms on the left side and squares both sides of the equation. This simplification allows us to express √√ in terms of √.

Finally, the resulting equation shows that √√ satisfies a polynomial equation with rational coefficients, proving that it is algebraic over Q. This contradicts the initial assumption that √√ is transcendental over Q, completing the proof.

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The account balance reaches 1,000,000 dollars approximately 65.79 years after it was opened.

The opening balance has already been calculated as 10

For when the account balance reach 1,000,000 dollars

We can set up the equation:

10e^(0.07t) = 1000

Dividing both sides by 10 gives:

e^(0.07t) = 100

Taking the natural logarithm of both sides gives:

0.07t = ln(100)

Divide both sides by 0.07

t = ln(100)/0.07

Evaluate

t ≈ 65.79

Therefore, the account balance reaches 1,000,000 dollars approximately 65.79 years after it was opened.

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Answer:

This illustrates a right triangle.

Given:

a(height) = 2457 ft.

∠A = 22°23' ; which is the elevation and reflects the a(height)

Find:

b(base)

Solution:

Using the law of cosine, specifically tan∠ = opposite side÷adjacent side

By analysis, tan∠A = a÷b

Since we are finding b, the formula will be derived into:

b = a÷tan∠A

Find b(base):

b = 2457 ft. ÷ tan22°23' ; substituting the numbers

b ≈ 5,966.05 ft. ; Final Answer

Step-by-step explanation:

Given:

The equation of the circle is:

\(x^2+y^2=16\)

To find:

The radius of the circle.

Solution:

The standard form of a circle is:

\((x-h)^2+(y-k)^2=r^2\)              ...(i)

Where, (h,k) is the center and r is the radius.

We have,

\(x^2+y^2=16\)

In can be written as:

\(x^2+y^2=4^2\)                 ...(ii)

On comparing (i) and (ii), we get

\(h=0\)

\(k=0\)

\(r=4\)

Here, the center of the circle is the origin and the radius is equal to 4 units.

Therefore, the radius of the given circle is 4 units.

tan 36° can be written as cot 54°, which simplifies to (√3 + 1) / (√3 - 1).

The tangent of 36° can be expressed in terms of its cofunction, which is the cotangent. The cotangent of an angle is equal to the reciprocal of the tangent of that angle. Therefore, we can rewrite tan 36° as cot (90° - 36°).

Now, cot (90° - 36°) can be simplified further. The angle 90° - 36° is equal to 54°. So, we have cot 54°.

The cotangent of 54° can be determined using the unit circle or trigonometric identities. In this case, the exact answer for cot 54° is (√3 + 1) / (√3 - 1).

Hence, tan 36° can be written as cot 54°, which simplifies to (√3 + 1) / (√3 - 1).

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Answer:

The solution is:

\(x=\frac{\sqrt{29}+7}{2},\:x=\frac{-\sqrt{29}+7}{2}\)

Step-by-step explanation:

Given the equation

\(x^2\:-7x=\:-5\)

\(\mathrm{Add\:}a^2=\left(-\frac{7}{2}\right)^2\mathrm{\:to\:both\:sides}\)

\(x^2-7x+\left(-\frac{7}{2}\right)^2=-5+\left(-\frac{7}{2}\right)^2\)

\(x^2-7x+\left(-\frac{7}{2}\right)^2=\frac{29}{4}\)

Apply perfect square rule

\(\left(x-\frac{7}{2}\right)^2=\frac{29}{4}\)

\(\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}\)

solving

\(x-\frac{7}{2}=\sqrt{\frac{29}{4}}\)

\(x-\frac{7}{2}=\frac{\sqrt{29}}{\sqrt{4}}\)

\(x-\frac{7}{2}=\frac{\sqrt{29}}{2}\)

\(\mathrm{Add\:}\frac{7}{2}\mathrm{\:to\:both\:sides}\)

\(x-\frac{7}{2}+\frac{7}{2}=\frac{\sqrt{29}}{2}+\frac{7}{2}\)

\(x=\frac{\sqrt{29}+7}{2}\)

also solving

\(x-\frac{7}{2}=-\sqrt{\frac{29}{4}}\)

\(\mathrm{Add\:}\frac{7}{2}\mathrm{\:to\:both\:sides}\)

\(x-\frac{7}{2}+\frac{7}{2}=-\frac{\sqrt{29}}{2}+\frac{7}{2}\)

\(x=\frac{-\sqrt{29}+7}{2}\)

Thus, the solution is:

\(x=\frac{\sqrt{29}+7}{2},\:x=\frac{-\sqrt{29}+7}{2}\)

Answer:

-11.2

Step-by-step explanation:

Answer:

48

Step-by-step explanation:

The amount of time needed and the amount of wall to paint are directly proportional. So, when we multiply the amount of wall to paint by 8/5 (going from 5000 square feet to 8000 square feet), we multiply the time needed by 8/5. Therefore, we need 30 * 8/5 = 48  minutes to paint the 8000 square foot wall.

We need 48 minutes to paint 8000 square football . The minute is a measure of time that is typically equal to 60 seconds, or 1/60 of an hour.

Given,

8 team members paint 5000square football in 30 min

So,

30*8/5

= 48 minutes

Therefore We need 48 minutes to paint 8000 square football.

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The code efficiently identifies prime numbers using the ancient Greek algorithm. It initializes an array, marks the multiples of each prime number as non-prime, and then prints the prime numbers.

This algorithm demonstrates a straightforward and efficient method for finding prime numbers within a given range.The ancient Greek algorithm for finding prime numbers less than or equal to a given number is implemented in the provided Python code. The algorithm follows a simple approach of marking numbers as prime or non-prime.

It starts by assuming all numbers as prime and then proceeds to mark the multiples of each prime number as non-prime. The code initializes an array where each element represents a number and marks them all as prime initially. Then, it iterates over each number from 2 to the given number, checking if it is marked as prime. If it is, the algorithm crosses out all its multiples as non-prime. Finally, it prints the numbers that remain marked as prime.

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Answer:

140.00

Step-by-step explanation:

20 x 4 = 80 hours worked

80 x 8.00 = $640.00

640.00 - 500.00 = 140.00

Answer:

x=5

Step-by-step explanation:

i took 12 and subtracted 7 to see what i got and to check my answer i added 5 to 7 to see if i got 12

Consider that we need to find \((a+b)(x), (a-b)(x), (ab)(x),\left(\dfrac{a}{b}\right)(x)\).

Given:

The functions are:

\(a(x)=4x+9\)

\(b(x)=3x-5\)

To find:

The function operations \((a+b)(x), (a-b)(x), (ab)(x),\left(\dfrac{a}{b}\right)(x)\).

Solution:

We have,

\(a(x)=4x+9\)

\(b(x)=3x-5\)

Now,

\((a+b)(x)=a(x)+b(x)\)

\((a+b)(x)=4x+9+3x-5\)

\((a+b)(x)=7x+4\)

Similarly,

\((a-b)(x)=a(x)-b(x)\)

\((a-b)(x)=4x+9-(3x-5)\)

\((a-b)(x)=4x+9-3x+5\)

\((a-b)(x)=x+14\)

And,

\((ab)(x)=a(x)b(x)\)

\((ab)(x)=(4x+9)(3x-5)\)

\((ab)(x)=12x^2-20x+27x-45\)

\((ab)(x)=12x^2+7x-45\)

And,

\(\left(\dfrac{a}{b}\right)(x)=\dfrac{a(x)}{b(x)}\)

\(\left(\dfrac{a}{b}\right)(x)=\dfrac{4x+9}{3x-5}\)

Therefore, the required functions are \((a+b)(x)=7x+4\), \((a-b)(x)=x+14\), \((ab)(x)=12x^2+7x-45\) and \(\left(\dfrac{a}{b}\right)(x)=\dfrac{4x+9}{3x-5}\).

Answer:

The number is 13

Step-by-step explanation:

the equation:

\(2x-6=20\)

The solution.

\(2x=20+6\)

\(x=\frac{26}{2} =13\)

Hope this helps

9514 1404 393

Answer:

  t = 1 1/7 ≈ 1.1429 seconds

Step-by-step explanation:

Filling in the given height, we can solve for t:

  640 = -490t^2 +1120t

  49t^2 -112t +64 = 0 . . . . . divide by 10, put in standard form

  (7t -8)^2 = 0

  t = 8/7 . . . . . . . the value of t that makes the factor(s) zero

The model rocket will reach its maximum height of 640 cm after 1 1/7 seconds.